President Obama and the National Institutes of Health have launched the Precision Medicine Initiative with the objective of developing targeted treatments to individual patients on the basis of their own genetics, environments, and lifestyles. To accomplish this goal the biomedical research community is collecting an exponentially increasing amount of clinical, genetic, genomic, and other high-dimensional data. While the data sets are rich, there remain substantial statistical and computational hurdles in optimally leveraging them to produce clinically meaningful information. In this talk I will describe several open problems that are both challenging and central to the field of medical genetics.